Two years of high schoolLatin are sufficient to translate the first few verses from the Vulgate, the Latin version of the Bible that was assembled in the 4th century from available Greek texts. "In the beginning God created heaven, and earth. And the earth was void and empty, and darkness was upon the face of the deep; and the spirit of God moved over the waters. And God said: Be light made. And light was made. And God saw the light that it was good; and he divided the light from the darkness. And he called the light Day, and the darkness Night; and there was evening and morning one day."[2] (Click for larger image.)

According to classical physics, photons should not have momentum, since they are massless and the momentum is the mass multiplied by velocity. In 1871, Maxwell calculated that electromagnetic radiation will exert a force on objects, a theory that was experimentally confirmed by Pyotr Lebedev in 1899. The photon momentum p in a vacuum is given as p = hk/2π, where h is Planck's Constant, and k is the wave vector. The wave vector has a value of 2π/λ, where λ is the wavelength, so shorter wavelengths have higher momentum.

It was subsequently discovered that the paddle wheel didn't move in a better vacuum, and a certain airpressure was needed to produce an optimal motion.

Careful thought would have indicated that the paddle wheel motion was in the opposite sense to what should be expected, since photons bouncing from the reflective surfaces would exert more force than those absorbed by the dark surfaces.

As I wrote in an earlier article (The Yarkovsky Effect, June 12, 2012), radiation pressure can be used to steer asteroids away from the Earth. The Yarkovsky effect is the photon momentum effect when photons are emitted by an object, rather than impinging upon it. A temperature difference of one side of an object versus the other causes an imbalance in its thermal radiation, and this results in a small force. The anisotropic emission of thermal photons in the Yarkovsky effect has been proposed as a method of steering asteroids away from collision with the Earth.

While the momentum of light in a vacuum is well established, there's the further question of the momentum of light in a dielectric. Since the speed of light is reduced in a dielectric by a factor equal to the refractive index, our classical mechanical sensibilities would conclude that the momentum of light is reduced by the same factor; that is, p = hk/2πn, where n is the refractive index. This is the value calculated by Max Abraham in 1909.[5] However, Hermann Minkowski calculated a momentum value p = nhk/2π in 1908.[6]

These two theoretical predictions differ by the square of the dielectric constant; so, you would think that the matter would have been experimentally resolved after more than a century. We still don't know, and it appears that the values obtained might even depend on the type of experiment used to make the measurement.[7-9] That's because the calculations done by Minkowski and Abraham assume an idealized case that combines the real and imaginarycomponents of the dielectric constant, while experiments partition the transfer of photon momentum differently for the real and imaginary parts of the refractive index.

Vortex beams present a donut-like shape when imaged on a surface, and torqued light beams show a croissant shape.[13] While the self-torque phenomenon can occur when electromagnetic fields interact with matter, there has been no optical analog until now.[11-12] The self-torque of light is an inherent property of the light, itself.[12] The research team demonstrated self-torque using beams in the extreme-ultraviolet that were driven by time-delayed pulses of different OAM.[12]

The torqued light beams were generated by the interference of two vortex beams of different orbital angular momentum.[11] A time delay between the OAM pulses produced a time-dependent angular momentum, the self-torque.[11] The self-torqued beams are created by high harmonic generation in which an ultrafast laser pulse is coherentlyupconverted into extreme-ultraviolet and X-rayspectra.[11] The self torque is a function of the OAM amplitude of the generating beams, their relative time delay, and the harmonic order.[11]